54 ELECTRIC RAILWAY ENGINEERING

consideration in the accurate calculation of speed time curves as
follows:

The energy of rotation—

*"""'- (25)

since

/ = M& (26)

where & = Angular velocity.
I = Moment of inertia.
M = Mass.
k = Radius of gyration.

These fundamental formulas will be applied to this particular
problem with the following nomenclature:

nw = Number of pairs of wheels on car.
na = Number of armatures on car.
Ww = Weight of each pair of wheels and axle in tons.
Wa = Weight of each armature in tons.
kw = Radius of gyration of wheels and axle.
ka = Radius of gyration of armature.
r — Radius of wheels in feet.
A = Acceleration of car in m.p.h./sec.
V = Velocity of car in ft. per sec.
i) = Velocity at extremity of radius of gyration.
g = Acceleration of gravity.
G = Gear ratio.
W = Weight of car in tons.
p = Net tractive effort at periphery of wheel.
Considering first the wheels and axles :
From Eq. (25)

Eu

But
Substituting

2g

= v

Ew =

(27)
(28)
(29)

Since the velocity of the periphery of the car wheel is the same
as that of the car, if it be assumed that no slipping occurs,
~\J(7 /lr \ 2
W./*«Tr\ (3())